How do you write the polar equation $theta=pi/3$ in rectangular form?

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Answer 1 · 2016-11-08T20:21:24

Please see the explanation for steps leading to the equation:
$y = (tan^-1(pi/3))x$

Substitute $tan(y/x)$ for $theta$

$tan(y/x) = pi/3$

Obtain $y/x$ on the left by using the inverse tangent on both sides:

$tan^-1(tan(y/x)) = tan^-1(pi/3)$

$y/x = tan^-1(pi/3)$

Multiply both sides by x:

$y = (tan^-1(pi/3))x$

Answer 2 · 2016-11-09T09:31:33

$y =sqrt3x$

The relation between polar coordinates $(r,theta)$ and Cartesian rectangular coordinates $(x,y)$ is given by

$x=rcostheta$ , $y=rsintheta$ and $tantheta=y/x$

As $theta=pi/3$ , we have $tantheta=sqrt3$

and equation is

$y/x=sqrt3$

Multiply both sides by $x$

$y =sqrt3x$

How do you write the polar equation theta=pi/3theta=pi/3 in rectangular form?